Problem: The learning rate for new skills is proportional to the difference between the maximum potential for learning that skill, $M$, and the amount of the skill already learned, $L$. Which equation describes this relationship? Choose 1 answer: Choose 1 answer: (Choice A) A $L(t)=k(M-L)$ (Choice B) B $L(t)=\dfrac{k}{(M-L)}$ (Choice C) C $\dfrac{dL}{dt}=k(M-L)$ (Choice D) D $\dfrac{dL}{dt}=\dfrac{k}{(M-L)}$
Solution: The amount of the skill already learned is denoted by $L$. The rate of change of the amount is represented by $L'(t)$, or $\dfrac{dL}{dt}$. Saying that the rate of change is proportional to something means it's equal to some constant $k$ multiplied by that thing. That thing, in our case, is the difference between the maximum potential, $M$, for learning that skill and the amount, $L$, of the skill already learned. In conclusion, the equation that describes this relationship is $\dfrac{dL}{dt}=k(M-L)$.